st Prep A new mobile device has a value of \( \$ 256.25 \). Its value changes by \( -22 \frac{1}{2} \% \) each year. What is the value of the phone after two years? \( \begin{array}{ll}\text { (A) } \$ 140.93 & \text { (C) } \$ 153.91 \\ \text { (B) } \$ 198.59 & \text { (D) } \$ 57.66\end{array} \)
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To find the value of the mobile device after two years with a depreciation of \( -22 \frac{1}{2} \% \) each year, you can calculate the value for each year separately. First, convert \( 22 \frac{1}{2} \% \) to a decimal: \( 22 \frac{1}{2} \% = 22.5\% = 0.225 \). Now calculate the value after the first year: \( V_1 = 256.25 \times (1 - 0.225) = 256.25 \times 0.775 = 198.59 \). For the second year, use the new value: \( V_2 = 198.59 \times (1 - 0.225) = 198.59 \times 0.775 \approx 153.91 \). Therefore, the value of the phone after two years is approximately \( \$ 153.91 \). Answer: (C) \$ 153.91. When it comes to depreciation, calculating the percentage decrease year over year is essential! Keep in mind that each year's value is based on the previous year's result, which can make a big difference in calculations—think of it as a snowball effect, reducing in both size and speed! If you're looking to deepen your understanding of percentage calculations, check out resources on financial literacy. Concepts like compound depreciation, interest rates, and total asset value can be fun to explore. Interactive tools and apps make it even more enjoyable!
